Assignment:
Question 1. A manufacturing company produces rods. Each rod is required to be 20 millimeters in diameter. Each hour, random samples of size n = 4 rods are measured to check process control. Five hours of observations yielded the following:
Diameter
Time Rod 1 Rod 2 Rod 3 Rod 4
9 A.M. 19.8 20.4 19.9 20.3
10 A.M. 20.1 20.2 19.9 19.8
11 A.M. 19.9 20.5 20.3 20.1
Noon 19.7 19.8 20.3 20.2
1 P.M. 19.7 20.1 19.9 19.9
Using these data and the table below, construct limits for xbar- and R-charts. Is the process in control?
Control Chart Limits Factors
Sample Size
n Mean Factor(A2) Upper Range(D4) Lower Range (D5)
2 1.880 3.628 0
3 1.023 2.574 0
4 0.729 2.282 0
5 0.577 2.114 0
6 0.483 2.004 0
7 0.419 1.924 0.076
8 0.373 1.864 0.136
9 0.337 1.816 0.184
10 0.308 1.777 0.223
12 0.266 1.716 0.284
Question 2. A p-chart has been developed for a particular item. In the past, 3% of such items have been found to be defective. If a sample of 100 is taken, and 9 of these are found to be defective, should the process be considered out of control? Explain.
Provide complete and step by step solution for the question and show calculations and use formulas.